Study Skills: Your Brain Can Learn Mathematics
1. Review of the Real Number System
1.1 Basic Concepts
1.2 Operations on Real Numbers
1.3 Exponents, Roots, and Order of Operations
1.4 Properties of Real Numbers
Study Skills: Using Your Textbook
2. Linear Equations and Applications
2.1 Linear Equations in One Variable
Study Skills: Homework: How, Why, When
2.2 Formulas and Percent
2.3 Applications of Linear Equations
Study Skills: Taking Lecture Notes
2.4 Further Applications of Linear Equations
Summary Exercises on Solving Applied Problems
Study Skills: Reviewing a Chapter
Study Skills: Preparing for Tests
3. Linear Inequalities and Absolute Value
3.1 Linear Inequalities in One Variable
Study Skills: Using Study Cards
3.2 Set Operations and Compound Inequalities
Study Skills: Using Study Cards Revisited
3.3 Absolute Value Equations and Inequalities
Summary Exercises on Solving Linear and Absolute Value Equations and Inequalities
Study Skills: Managing Your Time
Study Skills: Tips for Taking Math Tests
4. Graphs, Linear Equations, and Functions
4.1 The Rectangular Coordinate System
4.2 Slope of a Line
4.3 Linear Equations in Two Variables
4.4 Linear Inequalities in Two Variables
4.5 Introduction to Functions
Study Skills: Analyzing Your Test Results
5. Systems of Linear Equations
5.1 Systems of Linear Equations in Two Variables
5.2 Systems of Linear Equations in Three Variables
5.3 Applications of Linear Systems of Equations
5.4 Solving Linear Systems of Equations by Matrix Methods
6. Exponents, Polynomials, and Polynomial Functions
6.1 Integer Exponents and Scientific Notation
6.2 Adding and Subtracting Polynomials
6.3 Polynomial Functions
6.4 Multiplying Polynomials
6.5 Dividing Polynomials
7. Factoring
7.1 Greatest Common Factors; Factoring by Grouping
7.2 Factoring Trinomials
7.3 Special Factoring
7.4 A General Approach to Factoring
7.5 Solving Equations by Factoring
8. Rational Expressions
8.1 Rational Expressions and Functions; Multiplying and Dividing
Study Skills: Making a Mind Map
8.2 Adding and Subtracting Rational Expressions
8.3 Complex Fractions
8.4 Equations with Rational Expressions and Graphs
Summary Exercises on Operations and Equations with Rational Expressions
8.5 Applications of Rational Expressions
8.6 Variation
9. Roots, Radicals, and Root Functions
9.1 Rational Expressions and Graphs
9.2 Rational Exponents
9.3 Simplifying Radical Expressions
9.4 Adding and Subtracting Radical Expressions
9.5 Multiplying and Dividing Radical Expressions
Summary Exercises on Operations with Radicals
9.6 Solving Equations with Radicals
9.7 Complex Numbers
Study Skills: Preparing for Your Math Final
10. Quadratic Equations, Inequalities, and Functions
10.1 The Square Root Property and Completing the Square
10.2 The Quadratic Formula
10.3 Equations Quadratic in Form
Summary Exercises on Solving Quadratic Equations
10.4 Formulas and Further Applications
10.5 Graphs of Quadratic Functions
10.6 More About Parabolas and Their Applications
10.7 Polynomial and Rational Inequalities
11. Inverse, Exponential, and Logarithmic Functions
11.1 Inverse Functions
11.2 Exponential Functions
11.3 Logarithmic Functions
11.4 Properties of Logarithms
11.5 Common and Natural Logarithms
11.6 Exponential and Logarithmic Equations; Further Applications
12. Nonlinear Functions, Conic Sections, and Nonlinear Systems
12.1 Additional Graphs of Functions; Composition
12.2 The Circle and the Ellipse
12.3 The Hyperbola, and Other Functions Defined by Radicals
12.4 Nonlinear Systems of Equations
12.5 Second-Degree Inequalities and Systems of Inequalities
Appendix A. Strategies for Problem Solving
Appendix B. Review of Fractions
Appendix C. Synthetic Division
Answers to Selected Exercises
Solutions to Selected Exercises
Index